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A positive point charge Q is placed off-centre inside a neutral conducting shell centred at C, and a uniform external electric field E is then switched on. Which statement is correct?

1. The force on Q due to E is zero
2. The net force on Q is zero
3. The net force on the system of Q plus the conducting shell is zero
4. The net force on the shell due to E is zero

Correct answer: The net force on the system of Q plus the conducting shell is zero

Solution

Inside the cavity the external field is fully screened by the shell, yet Q is off-centre so the induced charges produce a non-uniform field on Q; therefore the net force on Q alone is not necessarily zero, and option about E acting directly is subtle. However, treating Q and the shell as one isolated system in electrostatic equilibrium, the internal forces are equal and opposite and the external uniform field produces equal and opposite surface forces, so the net force on the combined system is zero.

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